I hope you understand that this is a very vague question. If you'd just asked for dual-stick shooters or something specific like that, I could have given you a top 10 no problem. I'll take the question as it stands though and try to help you spend some of that tax money ;)

I'm on my phone right now, I'll add iTunes links when I'm on my iPad and have access to the iPad App Store.

These are my favorite iPad games, the ones that survive when all else get deleted:

Magic 2013: huge file size, but I've logged hundreds and hundreds of hours with this game. By far my favorite iPad game. Even when I have a new favorite game I'm addicted to, when I take a break I always come back to this. It's my favorite of my favorites.

Cave danmakus: Cave is a company that makes hyper-advanced 2D shooters (of the sub genre "danmaku") for arcade machines in Japan, and a few years ago they started porting their games to iOS. All of them are top-notch, the kind of stuff that raises the bar for what to look for on iOS, and I recommend them all highly. In specific, DODONPACHI MAXIMUM is a good entry point, with relatively simple gameplay and an easy to understand scoring system. Bug Princess would be another good place to start. DoDonPachi Resurrection and ESPGALUDA II are both super-deep, insanely hard, mega-competitive masterpieces, the kind of game you could spend years mastering. Finally, DEATHSMILES is a more casual experience (I mean that relatively, so it's still a very hardcore game), but the art is fantastic and there's an RPG mode with enough stat-augmenting equitable items to keep you busy collecting for a long, long time.

If you don't want to pay Cave prices, Phoenix HD is a supremely replayable pseudo-danmaku (I say "pseudo" because the game is randomized, unlike traditional danmakus) that's taken up way too much of my life. Also, Sunny Tam has two great danmakus with hyper-stylized visuals, called Danmaku Unlimited and Storm Strikers. Both are great.

If you're a fan of Edward Gorey, Corpse Craft is a must-buy tribute.

If you're into originality and quirky, creative games, Time Ducks will give you many smiles.

Zack Gage is the crown prince of indy games on iOS. Spell Tower is probably my favorite word game, and Bit Pilot is something you need to experience to appreciate. Also Halcyon is a musical little gem.

Speaking of indy, Jeff Minter (the three-decades-and-counting godfather of indy games) has some great stuff on iOS published by his company Llamasoft. They're all great, but my two favorite to play on iPad are Gridrunner and Super Ox Wars.

Eliss is still one of the best implementations of multitouch I've seen. Be warned, it gets hard, even if you have dexterous fingers.

Some people prefer playing Super Hexagon on a smaller screen, but I think my thumbs block too much on the iPhone. Whatever the device though, this game is mandatory.

In my opinion King of Dragon Pass is the single best long-term strategy game on iOS.

Perfect Cell is an inspired gem of a stealth game. It's a bit like a platformer, but your character ignores gravity, and the theme/story are grimmer and more adult than any platformer I've played.

Bit Dungeon is like an action-based roguelike mixed with the original Legend of Zelda, with a Diablo-esque loot system. It all adds up to creamy goodness.

Galaxy on Fire 2 is a fantastic 3D space adventure/rpg/shooter. There's a reason it's so popular.

If you're into card/board-type games, I recommend Neuroshima Hex for brow-furrowing strategy. Also, Playdek has some great card games; Ascension is my second-favorite iOS card game (after Magic 2013), Nightfall is also great (especially if you like monsters), and Penny Arcade The Game: Gamers vs. Evil is also very good (and I didn't even know the comic existed until after I enjoyed the game, so it's not just a dumb licensed property).

One last favorite for this list--Might & Magic Clash of Heroes is a fantastic strategy game, with console-level depth and features.

Thanks, will check all of these out in a week or so. If you were to compile a top ten of arcade iOS games, what games would be in the list.
iOS decision making games like The Walking Dead are amazing too.

Here are some highlights for me (leaving out stuff over 1GB):
Chaos Rings 2 - Good JRPG, kinda pricy though
Ravenmark: scourge of Estellion - very good turn based tactics game
CoC: Wasted Land - Xcom style combat strategy
Bloons TD 5 - enjoyable high speed tower defense
Fieldrunners 2 - excellent tower defense with several modes
Final Fantasy Tactics: War of Lions - still a great game.
Carcassonne - The best board game translation to iPad there is.
Ghost Trick - adventure/puzzle with an enjoyable story
Dead Space - surprisingly good first person game, generally I don't care for that sort of thing on an iPad
Spectromancer - lane based card strategy game. by the Magic the Gathering guy

Ghost Trick? If you enjoyed that you might want to check out Touch Detective. I haven't played it but I've heard them favorably compared and its got the same free for the first chapter + buy the rest structure (a great way to handle demos for this kind of game).

I only have an iPhone, but I would highly recommend Ascension, Nightfall, and Starbase Orion.

Ascension and Nightfall are both iOS ports of meatspace deckbuilding games of the same names. Ascension is essentially competitive solitaire. It's very easy to learn, and a lot of fun. I would strongly recommend picking up the expansion, "Storm of Souls" first and foremost. Nightfall is essentially a distilled version of Magic: the Gathering free-for-all games. It requires almost no setup (you can spend 30 seconds drafting a few cards, or let the computer do it for you to start playing instantly). It's learning curve is a bit steep at first, but once you figure it out it's a blast. One thing I will warn you, though, is that the quality of the game drops sharply if you play with less than 4 players (it allows up to 5, including you) because of how the resource system works.

Starbase Orion is the old 4X game Master of Orion II with the serial numbers filed off. It's one of the best 4X games (Explore, Expand, Exploit, Exterminate) ever (the original franchise died when executive meddling made the third Master of Orion widely different from the previous, very successful titles). If you liked any of the Civilization games, you will like Starbase Orion.

I think you meant Osmos? If you mean the game about being an amoeba that has to survive long enough to be the biggest, I agree that it's a must buy. Hopefully it'll go on sale again, but it's beautiful challenging, and the music is magical.

Two iOS games I think everyone should have are Carcassonne and Osmos. Other good ones: Crosswords, Autumn Dynasty, The Creeps!, Fieldrunners, GTA Vice City, Crazy Taxi...I can list all day. I used to review apps. 148Apps is a great resource for finding good apps. Can an eye on the Editor's Choice list over there - http://www.148apps.com/editors-choice/